Problems 8801 to 8900

Table 2.179: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

8801	$y^{''} + y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.606

8802	$y^{''} + y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.855

8803	$y^{''} - y y^{'} = 2 x$	[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	✗	7.233

8804	$y^{'} - y^{2} - x - x^{2} = 0$	[_Riccati]	✓	5.803

8805	$y^{''} - y^{'} x - x y - x = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.755

8806	$y^{''} - y^{'} x - x y - 2 x = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.773

8807	$y^{''} - y^{'} x - x y - 3 x = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.801

8808	$y^{''} - y^{'} x - x y - x^{2} - x = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.101

8809	$y^{''} - y^{'} x - x y - x^{3} + 2 = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.256

8810	$y^{''} - y^{'} x - x y - x^{4} - 6 = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.237

8811	$y^{''} - y^{'} x - x y - x^{5} + 24 = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.211

8812	$y^{''} - y^{'} x - x y - x = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.845

8813	$y^{''} - y^{'} x - x y - x^{2} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.990

8814	$y^{''} - y^{'} x - x y - x^{3} = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.167

8815	$y^{''} - a x y^{'} - b x y - c x = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.938

8816	$y^{''} - a x y^{'} - b x y - c x^{2} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.877

8817	$y^{''} - a x y^{'} - b x y - c x^{3} = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.925

8818	$y^{''} - y^{'} - x y - x = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.303

8819	$y^{''} - y^{'} - x y - x^{2} = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.198

8820	$y^{''} - y^{'} - x y - x^{2} - 1 = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.334

8821	$y^{''} - y^{'} - x y - x^{2} - 1 = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.386

8822	$y^{''} - 2 y^{'} - x y - x^{2} - 2 = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.319

8823	$y^{''} - 4 y^{'} - x y - x^{2} - 4 = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.334

8824	$y^{''} - y^{'} - x y - x^{3} + 1 = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.123

8825	$y^{''} - 2 y^{'} - x y - x^{3} - x^{2} = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.374

8826	$y^{''} - y^{'} - x y - x^{3} + 2 = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.346

8827	$y^{''} - 2 y^{'} - x y - x^{3} + 2 = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.331

8828	$y^{''} - 4 y^{'} - x y - x^{3} + 2 = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.358

8829	$y^{''} - 6 y^{'} - x y - x^{3} + 2 = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.372

8830	$y^{''} - 8 y^{'} - x y - x^{3} + 2 = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.340

8831	$y^{''} - y^{'} - x y - x^{4} + 3 = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.407

8832	$y^{''} - y^{'} - x y - x^{3} = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.167

8833	$y^{''} - x y - x^{3} + 2 = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	3.059

8834	$y^{''} - x y - x^{6} + 64 = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	3.656

8835	$y^{''} - x y - x = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.736

8836	$y^{''} - x y - x^{2} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	4.521

8837	$y^{''} - x y - x^{3} = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.573

8838	$y^{''} - x y - x^{6} - x^{3} + 42 = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	3.893

8839	$y^{''} - x^{2} y - x^{2} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.784

8840	$y^{''} - x^{2} y - x^{3} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	11.035

8841	$y^{''} - x^{2} y - x^{4} = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.879

8842	$y^{''} - x^{2} y - x^{4} + 2 = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.941

8843	$y^{''} - 2 x^{2} y - x^{4} + 1 = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.987

8844	$y^{''} - x^{3} y - x^{3} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.694

8845	$y^{''} - x^{3} y - x^{4} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	36.838

8846	$y^{''} - x^{2} y^{'} - x^{2} y - x^{2} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.093

8847	$y^{''} - x^{3} y^{'} - x^{3} y - x^{3} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.177

8848	$y^{''} - y^{'} x - x y - x = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.799

8849	$y^{''} - x^{2} y^{'} - x y - x^{2} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.200

8850	$y^{''} - x^{2} y^{'} - x^{2} y - x^{3} - x^{2} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.122

8851	$y^{''} - x^{2} y^{'} - x^{3} y - x^{4} - x^{2} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.182

8852	$y^{''} - \frac{y^{'}}{x} - x y - x^{2} - \frac{1}{x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	10.594

8853	$y^{''} - \frac{y^{'}}{x} - x^{2} y - x^{3} - \frac{1}{x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.955

8854	$y^{''} - \frac{y^{'}}{x} - x^{3} y - x^{4} - \frac{1}{x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	100.115

8855	$y^{''} - x^{3} y^{'} - x y - x^{3} - x^{2} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.081

8856	$y^{''} - x^{3} y^{'} - x^{2} y - x^{3} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.039

8857	$y^{''} - x^{3} y^{'} - x^{3} y - x^{4} - x^{3} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.043

8858	$y^{'''} - x^{3} y^{'} - x^{2} y - x^{3} = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.084

8859	$y^{''} + c y^{'} + k y = 0$	[[_2nd_order, _missing_x]]	✓	1.427

8860	$w^{'} = - \frac{1}{2} - \frac{\sqrt{1 - 12 w}}{2}$ i.c.	[_quadrature]	✓	3.162

8861	$y^{''} + y = \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.754

8862	$y^{''} + y = \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.737

8863	$y^{''} + y = \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.023

8864	$y^{''} + y = \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.764

8865	$y^{''} + y = \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.737

8866	$y^{''} + y = \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.874

8867	$y^{''} + y = \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.993

8868	$y^{''} + y = \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.893

8869	$y^{''} + y^{'} + y = \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.894

8870	$y^{''} + y^{'} + y = \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.067

8871	$y^{''} + y^{'} + y = \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.968

8872	$y^{'''} + y^{'} + y = x$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓	0.596

8873	$x^{4} y^{''} + x^{3} y^{'} - 4 x^{2} y = 1$	[[_2nd_order, _with_linear_symmetries]]	✓	1.764

8874	$x^{4} y^{''} + x^{3} y^{'} - 4 x^{2} y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	1.745

8875	$x^{2} y^{''} + y^{'} x - 4 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	1.156

8876	$x^{4} y^{'''} + x^{3} y^{''} + x^{2} y^{'} + x y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.221

8877	$x^{4} y^{'''} + x^{3} y^{''} + x^{2} y^{'} + x y = x$	[[_3rd_order, _with_linear_symmetries]]	✓	4.307

8878	$5 x^{5} y^{''''} + 4 x^{4} y^{'''} + x^{2} y^{'} + x y = 0$	[[_high_order, _with_linear_symmetries]]	✓	0.314

8879	$(x^{2} + 1) y^{''} + 1 + {y^{'}}^{2} = 0$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.949

8880	$(x^{2} + 1) y^{''} + 1 + {y^{'}}^{2} = x$	[[_2nd_order, _missing_y]]	✗	397.279

8881	$(x^{2} + 1) y^{''} + 1 + x {y^{'}}^{2} = 1$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.649

8882	$(x^{2} + 1) y^{''} + y {y^{'}}^{2} = 0$	[NONE]	✗	0.247

8883	$(x^{2} + 1) y^{''} + {y^{'}}^{2} = 0$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.670

8884	$y^{''} + \sin (y) {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.917

8885	$(x^{2} + 1) y^{''} + {y^{'}}^{3} = 0$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.986

8886	$y^{'} = e^{- \frac{y}{x}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	1.940

8887	$y^{'} = 2 x^{2} \sin {(\frac{y}{x})}^{2} + \frac{y}{x}$	[[_homogeneous, ‘class D‘]]	✓	3.394

8888	$4 x^{2} y^{''} + y = 8 \sqrt{x} (1 + \ln (x))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.642

8889	$v v^{'} = \frac{2 v^{2}}{r^{3}} + \frac{λ r}{3}$	[_rational, _Bernoulli]	✓	2.102

8890	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.661

8891	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.799

8892	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = x + 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.735

8893	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = x$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.773

8894	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = x^{2} + x + 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.854

8895	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = x^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.708

8896	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = x^{2} + 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.942

8897	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = x^{4}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.897

8898	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.762

8899	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = 1 + \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.943

8900	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = x \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.905

2.2.89 Problems 8801 to 8900